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Question

Find the size distance and Nature of image formed of an object size 1cm height a distance 15cm infront of concave mirror of focal length.

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Solution

Focal length is not given in the question.But I have seen this question before and the value of focal length=10 cm.This information is missing and please make a note that focal length=10 cm.

The given mirror is a concave mirror ,thus by sign convention it's focal length will be negative.

f = -10 cm
u = -15cm
h(height of object) = 1cm

we have to find
size , nature , distance of image formed .

Thus using mirror equation :-
1/f = 1/u+1/v
=>1/v = 1/f-1/u
=> 1/v = -1/10+1/15
=> 1/v = -1/30
=> v = -30 cm{ thus image will be formed at a distance of 30 cm in front of the mirror}
Now magnification
m = -(v/u) = h'/h
m = -(-30/-15)
=> m = -2
HENCE the nature of image formed will be real and inverted (due to negative sign)and magnified.

Now m = h'/h
2 = h'/1
=> h' = 2cm
hence the size of the image will be doubled.

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